The news for Europe's banks doesn't get a lot better, with this morning's downgrade of the credit ratings of Portugal's banks by Moody's - on concerns about the quality of their big loans to the Portuguese government (inter alia).

And for the UK, the long expected downgrade (also by Moody's) of the credit ratings of Royal Bank of Scotland, Lloyds TSB (sic), Santander and a number of smaller banks and building societies has taken place - which, I have to say, I regard as of lesser significance.

The point is that the UK banks' downgrade is an inevitable consequence of government policy to reduce the likelihood that they would be bailed out in a crisis - of which the most conspicuous manifestation has been the Vickers' commission recommendations to put retail banks behind a ring fence and make creditors to banks explicitly liable to losses.

So, in a sense, the downgrades should be viewed as a good thing, if they reflect a genuine transfer of risk from taxpayers to the banks' creditors. The important point, for today however, is that these downgrades have been anticipated and discounted by the market for some time, so their real economic impact on the affected banks should be negligible.

Or to put it another way, these banks are already paying more to fund themselves, to reflect the perceived increase in the risks faced by those who finance them.

But what about the wider problem of the perceived weakness of the eurozone's banks, which is the faultline running through the global economy right now?

Health checks

If the eurozone does turn the current jaw-jaw into a war-war against the weakness of banks' balance sheets, how much capital would European banks be forced to raise - and which big banks would be forced to raise the most?

Well the French financial firm, Natixis, has done a quick, dirty and gripping analysis.

It has made a number of assumptions about the parameters that would be used by the European Banking Authority for determining the amount of capital that would need to be injected into banks, to protect them against potential future losses.

Natixis assumes the following percentage writedowns (or "marks") on Greek, Irish, Portuguese, Italian and Spanish debt, respectively: 70%, 40%, 40%, 20% and 20%. And then it assumes the banks would need to preserve a core tier one ratio of either 7% or 8% on these stressed scenarios by the end of 2012.

Now on that basis, the European banking sector would have to raise €90bn to maintain core equity capital at 7% of assets, or €182bn for 8%.

Now what is quite striking is that on Natixis's calculations, the banks that would have to raise the most capital are from Italy and Greece, for the obvious reason that they have greatest exposure to their respective governments, and from Germany. But, interestingly, French banks would be in need of less capital.

Here is Natixis's league table of which banks need what:

Commerbank of Germany would need €4.6bn to preserve a 7% capital ratio and €7.7bn at 8%;

Deutsche of you-know-where would need €3.1bn for 7% and €8.1bn for 8%;

Italy's Unicredit would need a staggering €7.2bn and €12.5bn;

BBVA and Santander of Spain would need nudging €4bn each if the capital threshold were set at 8%, but negligible amounts at 7%;

BNP would need €6.2bn at 8% and nothing at 7%;

Soc Gen would need €2.9bn for 7% and €7.3bn for 8%.

What conclusions flow from this?

That a Europe-wide capital-raising exercise could be painful for the Germans. And if ministers want to do what investors and creditors apparently want them to do, which is to force a serious recapitalisation of big French banks, the minimum capital threshold would have to be set high, at 8%.

Given that these measures to strengthen banks will almost certainly apply to all EU banks, not just eurozone banks, what impact would they have on British banks.

If the minimum stressed capital ratio were set at 8%, Royal Bank of Scotland, Barclays and Lloyds would all be forced to raise new capital.

Among the British banks Royal Bank of Scotland is most vulnerable to being forced to raise new capital, because under July's health checks its stressed capital ratio emerged relatively low at 6.3% (compared with 7.3% for Barclays, 7.7% for Lloyds and 8.5% for HSBC).

So if the new minimum capital bar were set at 7% (and we have no idea where it will ultimately be set) RBS would seem to need to raise a few billions of additional capital.

Taxpayer loss

But there are a couple of important riders.

The first is that RBS would claim that the original stress test made it look much weaker than is really the case: in assessing RBS's vulnerability to future losses on financial trading, an average was taken of its losses over the past few years, during which RBS incurred record-breaking, eye-watering losses on financial trading; and since then its trading book has shrunk very considerably and become much less risky.

So the stress tests' methodological approach of averaging recent trading losses would exaggerate RBS's current fragility and vulnerability to loss - and in a sense would discriminate against it.

The interesting question is whether other European governments will take any heed of this, as and when the Treasury argues that RBS is stronger than it looks.

What happens if RBS were forced to raise additional capital?

Well that would be quite bad news for taxpayers. Because under the terms of its government bailout, RBS has the right to sell new shares to the government at 50p per share, or roughly twice the current price (in technical terms, 50p is the conversion price of RBS's 'B' shares).

In other words, taxpayers would incur massive losses on an injection of capital into RBS which may well be a needless injection of capital.

I would therefore expect the chancellor to argue pretty strongly to his eurozone counterparts that RBS has quite enough capital for now.

And if he were to lose this battle, he might well be better off launching a takeover bid to acquire all of RBS - to nationalise it fully - than recapitalising the bank through an exercise of the existing rescue mechanism.